Quantum (sl_n, \land V_n) link invariant and matrix factorizations

Abstract

M. Khovanov and L. Rozansky gave a categorification of the HOMFLY-PT polynomial. This study is a generalization of the Khovanov-Rozansky homology. We define a homology associated to the quantum $(s{l}_n,\wedge V_n)$ link invariant, where $\wedge V_n$ is the set of the fundamental representations of the quantum group of $s{l}_n$. In the case of a [1,k]-colored link diagram, we prove that its homology is a link invariant. In the case of an [i,j]-colored link diagram, we define a normalized Poincare polynomial of its homology and prove the polynomial is a link invariant.

Doctoral thesis (October, Nagoya University)

References in corpus (1)

• Knot homology via derived categories of coherent sheaves II, sl(m) case

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